Test sets for languages of infinite words

Abstract

We prove that any set of equations on infinite words in a finite number of indeterminates has, over a countably generated free monoid, a finite equivalent subsystem. From this it follows that any language L of finite and infinite words on a finite alphabet A has a test set for morphisms from A∞ to B∞. In the case of finite words, the result has been proved by Albert and Lawrence (“A proof of Ehrenfeucht's conjecture”, 1985).